Finite Group Databasebeta

← #21450707

Subgroups — #21450707

Order 7808.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519759C211yesmaximal, characteristic, complemented
2C2×#14519745C211yesmaximal, characteristic
3C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
5#16839686C211yesmaximal, characteristic, complemented
6#16839685C211yesmaximal, characteristic, complemented
7#16839677C211yesmaximal, characteristic, complemented
8#16839676C211yesmaximal, characteristic, complemented
9#16839654C211yesmaximal, characteristic, complemented
10#16839650C211yesmaximal, characteristic, complemented
11#16839641C211yesmaximal, characteristic, complemented
12#16839624C211yesmaximal, characteristic, complemented
13#16839621C211yesmaximal, characteristic, complemented
14#16839617C211yesmaximal, characteristic, complemented
15C61×#386C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21#14519759—24no—
22#14519745—24no—
23C4×C22⋊D61—24no—
24C2×C4⋊Dic61C2211yescharacteristic, complemented
25C2×#11758196C2211yescharacteristic, complemented
26C2×#11758196C2211yescharacteristic, complemented
27C2×#11758196C2211yescharacteristic, complemented
28C2×#11758196C2211yescharacteristic, complemented
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic, complemented
33C2×C22⋊Dic61C2211yescharacteristic, complemented
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C22⋊C4×D61—24no—
43C2×C4×Dic61C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48C22×D4×C61C2211yescharacteristic
49C23×C4×C61C2211yescharacteristic, complemented
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic, complemented
53#95×C61C2211yescharacteristic, complemented
54#95×C61C2211yescharacteristic, complemented
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C23×D61—22no—
58C23×D61—22no—
59C23×D61—22no—
60C23×D61—22no—
61C23×D61—22no—
62C23×D61—41no—
63C23×D61—41no—
64C23×D61C2311yescharacteristic
65C23×D61C2311yescharacteristic
66C2×D4×C61—22no—
67C2×D4×C61—22no—
68C2×D4×C61—41no—
69C22×C4×C61—22no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C2×C22⋊D61—22no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—22no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61D414yes—
83C22×Dic61C2311yescharacteristic
84C22×Dic61C2311yescharacteristic
85C22×Dic61C2311yescharacteristic
86C22×Dic61C2311yescharacteristic
87C22×Dic61C2311yescharacteristic
88C22×Dic61C2311yescharacteristic
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
94C2×C4×D61D414yescomplemented
95C22⋊C4×C61—22no—
96C22⋊C4×C61—22no—
97C22⋊C4×C61—41no—
98C22⋊Dic61—22no—
99C22⋊Dic61—22no—
100C22⋊Dic61—22no—
101C22⋊Dic61—22no—
102C22⋊Dic61—22no—
103#11758198—22no—
104#11758198—22no—
105#11758198—22no—
106#11758198—22no—
107#11758198—22no—
108#11758198—22no—
109#11758198—22no—
110#11758198—41no—
111C4⋊Dic61—22no—
112#11758196—22no—
113#11758196—22no—
114#11758196—41no—
115#11758196—41no—
116C4×Dic61—22no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61C2×D412yes—
130C23×C61#4112yes—
131C23×C61C2411yescharacteristic
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—28no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—44no—
144C22×D61—44no—
145C22×D61—44no—
146C22×D61—44no—
147C22×D61—44no—
148C22×D61—44no—
149C22×D61C2×D412yes—
150C22×D61C2×D412yes—
151C22×D61#4112yes—
152C22×D61#4112yes—
153D4×C61—44no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—44no—
169C2×C4×C61C2×D412yes—
170C22⋊D61—28no—
171C22⋊D61—44no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61C2×D412yes—
189C2×Dic61C2×D412yes—
190C4×D61—44no—
191C4×D61—44no—
192C22×C61—22no—
193C22×C61—22no—
194C22×C61—22no—
195C22×C61—22no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61C22×D411yescharacteristic
207C22×C61C22×D411yescharacteristic
208C22×C61C2×#4111yescharacteristic
209C22×C61C2×#4111yescharacteristic
210C22×C61C2×#4111yescharacteristic
211C22×C61H(5,𝔽2)11yescharacteristic
212C22×C61H(5,𝔽2)11yescharacteristic
213C2×D61—22no—
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—22no—
218C2×D61—22no—
219C2×D61—22no—
220C2×D61—22no—
221C2×D61—22no—
222C2×D61—416no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61#12114yes—
228C4×C61—22no—
229C4×C61—41no—
230C4×C61—41no—
231C4×C61—41no—
232C4×C61—41no—
233Dic61—22no—
234Dic61—22no—
235Dic61—41no—
236Dic61—41no—
237Dic61—41no—
238Dic61—41no—
239#2534—611nomaximal, Sylow
240C2×C61—42no—
241C2×C61—42no—
242C2×C61C2×#12111yescharacteristic
243C2×C61#52511yescharacteristic
244C2×C61#53411yescharacteristic
245C2×C61#54611yescharacteristic
246C2×C61#54611yescharacteristic
247C2×C61#55111yescharacteristic
248C2×C61#55111yescharacteristic
249D61—24no—
250D61—42no—
251C2×#123—611no—
252C2×#120—611no—
253C2×C4×D4—611no—
254C22×C22⋊C4—611no—
255#396—611no—
256#396—611no—
257#394—611no—
258#394—611no—
259#388—611no—
260#388—611no—
261#386—611no—
262#386D6111yescharacteristic, complemented
263#381—611no—
264#380—611no—
265#379—611no—
266C61#253411yescharacteristic, complemented, Sylow
267C25—611no—
268C22×D4—611no—
269C22×D4—611no—
270C22×D4C2×D6111yescharacteristic
271C23×C4—611no—
272C23×C4—611no—
273C23×C4C2×D6111yescharacteristic, complemented
274#123—1224no—
275#120—1224no—
276C4×D4—1224no—
277C2×C4⋊C4—611no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—611no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—611no—
288C2×C22⋊C4—611no—
289C2×C22⋊C4—611no—
290C2×C22⋊C4—611no—
291C2×C22⋊C4—611no—
292C2×C22⋊C4—611no—
293C2×C22⋊C4—611no—
294C2×C22⋊C4—611no—
295C2×C22⋊C4—1224no—
296C2×C22⋊C4C2×D6111yescharacteristic
297C2×C22⋊C4C2×D6111yescharacteristic
298C2×C22⋊C4C2×D6111yescharacteristic, complemented
299C2×C42—611no—
300#95—611no—
301#95—611no—
302#95—611no—
303#95—611no—
304#95C2×D6111yescharacteristic, complemented
305#95C2×D6111yescharacteristic, complemented
306C24—611no—
307C24—611no—
308C24—1222no—
309C24—1222no—
310C24—1222no—
311C24—1222no—
312C24—1222no—
313C24—2441no—
314C24—2441no—
315C24C22×D6111yescharacteristic
316C24C22×D6111yescharacteristic
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—41no—
320C2×D4—614no—
321C2×D4—1222no—
322C2×D4—1222no—
323C2×D4—1222no—
324C2×D4—1222no—
325C2×D4—2441no—
326C22×C4—22no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—614no—
332C22×C4—611no—
333C22×C4—611no—
334C22×C4—611no—
335C22×C4—611no—
336C22×C4—1222no—
337C22×C4—1222no—
338C22×C4—1222no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4C22×D6111yescharacteristic
342C22×C4C22×D6111yescharacteristic
343C22×C4C22×D6111yescharacteristic
344C22×C4C22×D6111yescharacteristic
345C22×C4C22×D6111yescharacteristic
346C4⋊C4—1222no—
347C4⋊C4—1222no—
348C4⋊C4—1222no—
349C4⋊C4—2441no—
350C4⋊C4—2441no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—1222no—
355C22⋊C4—1222no—
356C22⋊C4—1222no—
357C22⋊C4—1222no—
358C22⋊C4—1222no—
359C22⋊C4—1222no—
360C22⋊C4—1222no—
361C22⋊C4—1222no—
362C22⋊C4—1222no—
363C22⋊C4—1222no—
364C22⋊C4—1222no—
365C22⋊C4—1222no—
366C22⋊C4—2441no—
367C42—1222no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—612no—
381C23—612no—
382C23—612no—
383C23—612no—
384C23—1228no—
385C23—1221no—
386C23—1221no—
387C23—1221no—
388C23—1221no—
389C23—1221no—
390C23—1221no—
391C23—1221no—
392C23—1221no—
393C23—1221no—
394C23—1221no—
395C23—2444no—
396C23—2444no—
397C23—2444no—
398C23—2444no—
399C23—2444no—
400C23—2444no—
401C23#1175822212yes—
402C23D4×D6112yes—
403C23C23×D6111yescharacteristic
404D4—44no—
405D4—1228no—
406D4—2444no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—44no—
422C2×C4—612no—
423C2×C4—612no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—2444no—
441C2×C4—2444no—
442C2×C4D4×D6112yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—614no—
458C22—1222no—
459C22—1222no—
460C22—1222no—
461C22—1222no—
462C22—1222no—
463C22—1222no—
464C22—1222no—
465C22—1222no—
466C22—1222no—
467C22—24416no—
468C22—2441no—
469C22—2441no—
470C22—2441no—
471C22—2441no—
472C22C2×D4×D6111yescharacteristic
473C22C2×D4×D6111yescharacteristic
474C22#41×D6111yescharacteristic
475C22#41×D6111yescharacteristic
476C22C2×#1175822211yescharacteristic
477C22#1451982211yescharacteristic
478C22#1451982211yescharacteristic
479C4—22no—
480C4—41no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—1222no—
485C4—1222no—
486C4—2441no—
487C4—2441no—
488C4—2441no—
489C4—2441no—
490C2—42no—
491C2—42no—
492C2—1224no—
493C2—2442no—
494C2#121×D6111yescharacteristic
495C2#1684027111yescharacteristic
496C2#1684032211yescharacteristic
497C2#1684040111yescharacteristic
498C2#1684040211yescharacteristic
499C2#1684044011yescharacteristic
500C2#1684044111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2534
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#14519759C2semidirect
3. C2×C4×C22⋊D61C2semidirect
4. C2×C22⋊C4×D61C2semidirect
5. #16839686C2semidirect
6. #16839685C2semidirect
7. #16839677C2semidirect
8. #16839676C2semidirect
9. #16839654C2semidirect
10. #16839650C2semidirect
11. #16839641C2semidirect
12. #16839624C2semidirect
13. #16839621C2semidirect
14. #16839617C2semidirect
15. C61×#386C2semidirect
24. C2×C4⋊Dic61C22semidirect
25. C2×#11758196C22semidirect
26. C2×#11758196C22semidirect
27. C2×#11758196C22semidirect
28. C2×#11758196C22semidirect
32. C2×C22⋊Dic61C22semidirect
33. C2×C22⋊Dic61C22semidirect
43. C2×C4×Dic61C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
49. C23×C4×C61C22semidirect
52. C2×C22⋊C4×C61C22semidirect
53. #95×C61C22semidirect
54. #95×C61C22semidirect
94. C2×C4×D61D4semidirect
262. #386D61semidirect
266. C61#2534semidirect
273. C23×C4C2×D61semidirect
298. C2×C22⋊C4C2×D61semidirect
304. #95C2×D61semidirect
305. #95C2×D61semidirect